Related papers: Proof Nets and the Identity of Proofs
"Systems that Explain Themselves" appears a provocative wording, in particular in the context of mathematics education -- it is as provocative as the idea of building educational software upon technology from computer theorem proving. In…
We discuss a practical method for assessing mathematical proof online. We examine the use of faded worked examples and reading comprehension questions to understand proof. By breaking down a given proof, we formulate a checklist that can be…
This lecture note focuses on comparing the notions of invariance and home spaces in Transition Systems and more particularly, in Petri Nets. We also describe how linear algebra relates to these basic notions in Computer Science, how it can…
Ontology embeddings map classes, roles, and individuals in ontologies into $\mathbb{R}^n$, and within $\mathbb{R}^n$ similarity between entities can be computed or new axioms inferred. For ontologies in the Description Logic…
The aim of these notes is to provide a succinct, accessible introduction to some of the basic ideas of category theory and categorical logic. The notes are based on a lecture course given at Oxford over the past few years. They contain…
We show that the proof nets introduced in [Hughes & van Glabbeek 2003, 2005] for MALL (Multiplicative Additive Linear Logic, without units) identify cut-free proofs modulo rule commutation: two cut-free proofs translate to the same proof…
Training machine learning (ML) models typically involves expensive iterative optimization. Once the model's final parameters are released, there is currently no mechanism for the entity which trained the model to prove that these parameters…
Artificial intelligence assisted mathematical proof has become a highly focused area nowadays. One key problem in this field is to generate formal mathematical proofs from natural language proofs. Due to historical reasons, the formal proof…
Protothetic is one of the most stimulating systems for propositional logic. Including quantifiers and an inference rule for definitions, it is a very interesting mean for the study of many questions of metalogic. Unfortunately, it only…
Unlike the flow structure of natural languages, programming languages have an inherent rigidity in structure and grammar.However, existing detection methods based on pre-trained models typically treat code as a natural language sequence,…
We present a prototype of an integrated reasoning environment for educational purposes. The presented tool is a fragment of a proof assistant and automated theorem prover. We describe the existing and planned functionality of the theorem…
The correct way to quantify predictive uncertainty in neural networks remains a topic of active discussion. In particular, it is unclear whether the state-of-the art entropy decomposition leads to a meaningful representation of model, or…
This paper is the second part of an introduction to linear logic and ludics, both due to Girard. It is devoted to proof nets, in the limited, yet central, framework of multiplicative linear logic and to ludics, which has been recently…
These lecture notes provide an introduction to the verification of neural networks from a theoretical perspective. We discuss feed-forward neural networks, recurrent neural networks, attention mechanisms, and transformers, together with…
This paper specifies an observational semantics and gives an original presentation of the Byrd box model. The approach accounts for the semantics of Prolog tracers independently of a particular Prolog implementation. Prolog traces are, in…
We discuss proving correctness and completeness of definite clause logic programs. We propose a method for proving completeness, while for proving correctness we employ a method which should be well known but is often neglected. Also, we…
Different automated theorem provers reason in various deductive systems and, thus, produce proof objects which are in general not compatible. To understand and analyze these objects, one needs to study the corresponding proof theory, and…
We define a fragment of propositional logic where isomorphic propositions, such as $A\land B$ and $B\land A$, or $A\Rightarrow (B\land C)$ and $(A\Rightarrow B)\land(A\Rightarrow C)$ are identified. We define System I, a proof language for…
In this work we present a computation paradigm based on a concurrent and incremental construction of proof nets (de-sequentialized or graphical proofs) of the pure multiplicative and additive fragment of Linear Logic, a resources conscious…
The features of a logically sound approach to a theory of statistical reasoning are discussed. A particular approach that satisfies these criteria is reviewed. This is seen to involve selection of a model, model checking, elicitation of a…